Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33460 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#508 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19,24,30)(20,32,21,27)(22,31,25,28)(23,38,40,46)(26,36,43,34)(29,37,47,41)(33,44,35,45)(39,48,49,42);(18,20,24,21)(19,26,30,43)(22,33,25,35)(23,39,40,49)(27,38,32,46)(28,42,31,48)(29,45,47,44)(34,37,36,41);(14,16,17,15)(18,21,24,20)(19,27,30,32)(22,33,25,35)(23,36,40,34)(26,38,43,46)(28,45,31,44)(29,42,47,48)(37,39,41,49);(18,22,24,25)(19,28,30,31)(20,33,21,35)(23,37,40,41)(26,42,43,48)(27,44,32,45)(29,46,47,38)(34,39,36,49)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26448);